Answer to Question #289718 in Statistics and Probability for Netu

Question

Two tetrahedral die with faces labelled 1,2,3and 4are thrown and the number on which each leads in noted the score is the sum of these two number.find the probability that (a)the score is even in seat at least one die lands on a 3

(b)at least one die lands on a 3,given that the score is even

Answer 1

Let A - ''the score is even", B - "at least one lands on 3", then

a) $P(A|B)={\frac {P(A\cap B)} {P(B)}}={\frac {{\frac 3 {16}}} {1-({\frac 3 4})^2}}={\frac 3 7}$

b)$P(B|A)={\frac {P(A\cap B)} {P(A)}}$

There are totally 16 outcomes when rolling two 4-sided dice, in 8 of which sum of the numbers is even, so

$P(A)={\frac 8 {16}}={\frac 1 2}$

so

$P(B|A)={\frac {{\frac 3 {16}}} {\frac 1 2}}={\frac 3 8}$